For me, the problem was always that I could never find salt cod that was hechshered. I have looked for years, and the Lasco salt cod that is ubiquitous on supermarket shelves was never certified kosher, and none of the specialty salt cods which I'd occasionally run into were, either. I would imagine that if one were to run into a piece with evidence of scales in the skin, that would be sufficient, given the possibility of ascertaining from the manufacturer that nothing other than salt was added, (or if it was, it would probably not be in the realm of "secret ingredient", and therefore would be disclosed.
Using fresh (or fresh frozen) cod instead of salt cod is totally acceptable. Salting cod was the only practical way of preserving it and reconstituting salted cod doesn't give you any real benefit over fresh, other than being "traditional." Also, much of what is passed off as salt cod is pollock and/or haddock -- both acceptable but not better than good cod, in my opinion. So get some fresh (or fresh frozen) and no one will notice but you.
If you're looking for a firmer texture then you can try "curing" fresh cod on your own, either with an overnightsoak in salted water or by covering in salt for several hours and then rinsing. It will "firm up" the texture much like curing salmon before smoking gives you a meatier texture.